Ascension and relative power levels
DNA3000
Member, Guardian Guardian › Posts: 19,841 Guardian
I was trying to make some ascension decisions the other day when I decided to actually calculate precisely where Ascended champs fall in the power spectrum of champion rarity. How does an ascended 6* compare to 7* champs? Are ascended 5* champs viable competitors to 6* champs? That sort of thing.
There's no way to do a perfect apples to apples comparison, because there are other factors at play. There's awakening and signature levels, for example. Lower rarity champs are easier to awaken and sig up. And then there are some other scaling effects that are difficult to perfectly quantify and compare - combat power rate, for example, or abilities that have their own scaling. So this is just looking at the factors we can compare - attack and health scaling.
Ascension scales champions attack and health upward by a fixed amount, although that amount differs by rarity. According to the table given in the Ascension announcement (https://playcontestofchampions.com/news/ascension/) 4* champs gain 30% attack and health when ascended, 5* champs gain 20%, and 6* champs gain 22%. If we focus on the percentage change and look at one of the two stats affected by Ascension, we can take a sample champ (I picked Angela, as she's available at 7*) and see how her attack value scales upward with rarity, rank, and ascension:
I've sorted in descending order from highest to lowest. This is what it looks like in pretty picture form:
We can see that Ascended 6* R5 is almost identical to 7* R2. I don't think that's a coincidence. I've color coded 7* champs in red, 6* champs in green (ascended champs in a lighter shade) 5* champs in blue, and 4* champs in brown. I'm not sure that helps, but there you go.
These numbers don't fully express the actual difference between rarities and ranks however. When you increase attack by 20% and health by 20%, you don't make the champ 20% stronger. Consider a fight where you are dealing damage and taking damage. You win if you deal enough damage to defeat the defender before you take enough damage to die. There is, in theory, a maximum amount of damage you can deal before you die, if you are constantly losing health. If you increase your attack by 20%, you will deal 20% more damage. But if you increase your health by 20%, you will also deal 20% more damage - because you will live longer and deal more damage before you die. If you increase both, your damage per second goes up and also how many seconds you live to deal damage goes up. The total amount of damage you can deal before you die goes up by a factor of 1.2 x 1.2 =1.44. So in situations where you are challenged and taking damage, increasing damage and health by 20% increases your overall damage dealing ability by almost 50%.
If we scale everyone down to where 5* R1 = 1.0, we can come up with a combined power table that reflects that combined benefit:
And of course:
Now, the order of the champions remains the same, because in effect all we're doing is squaring the numbers. If a < b, a^2 will also be smaller than b^2 (at least here, where power levels start at 1.0 and go up). So the order is the same, but the magnitude of the differences goes up substantially. 7* R2 and 6* R5 ascended look pretty close to 7* R3 in the one dimensional scaling table, but in the combined relative power table 7* R3 is far higher than both. This shows the exponential growth of champion power over time.
The first table does have uses. By focusing on one dimension, we can ask questions like "is a 6* R5 ascended running a 20% champion boost competitive with a 7* R3? The 6* R5 ascended is around 5000 and the 7* R3 is a bit above 6000, so yes, a 6* R5 Ascended champ running a 20% boost is going to be, at least when talking about health and attack, comparable to a 7* R3. Also, if you are in fights where you are pretty sure you aren't going to die, the main advantage of higher rarity is more damage and quicker kills. In that case, more health is not a noteworthy advantage and in those cases the first table better reflects the advantage differences between rarities.
But I think for most players in most reasonably challenging content, it is the second set of data that better quantifies the relative strengths of the different rarities and where ascension places champs, at least before considering the stats ascension does not affect the scaling of, like combat power rate, ability effects, critical rate, etc.
Overall, to me it does look like Ascension roughly does the job it was intended to do. If you're a player that is currently using a mix of 5* and 6* champs, then 5* R5 ascended is at least competitive with a 6* R3, and for such players 6* R4s will likely be still difficult to get. For players using mixes of 6* and 7* champs 6* R5 ascended is very competitive with 7* R2, with 7* R3 champs currently extremely constrained - but those highly expensive and difficult to get rank ups are standing head and shoulders above the rest, as they currently should.
Presumably, almost no one is going to ascend champs that are not either at max rank or one tier below, but I put them all in there for completeness. But I think the best candidates for Ascension are 6* R5, 6* R4, 5* R5, 4* R5, and maybe 6* R3 and 5* R4 (for lower progress players). i would not recommend ascending other ranks.
There's no way to do a perfect apples to apples comparison, because there are other factors at play. There's awakening and signature levels, for example. Lower rarity champs are easier to awaken and sig up. And then there are some other scaling effects that are difficult to perfectly quantify and compare - combat power rate, for example, or abilities that have their own scaling. So this is just looking at the factors we can compare - attack and health scaling.
Ascension scales champions attack and health upward by a fixed amount, although that amount differs by rarity. According to the table given in the Ascension announcement (https://playcontestofchampions.com/news/ascension/) 4* champs gain 30% attack and health when ascended, 5* champs gain 20%, and 6* champs gain 22%. If we focus on the percentage change and look at one of the two stats affected by Ascension, we can take a sample champ (I picked Angela, as she's available at 7*) and see how her attack value scales upward with rarity, rank, and ascension:
I've sorted in descending order from highest to lowest. This is what it looks like in pretty picture form:
We can see that Ascended 6* R5 is almost identical to 7* R2. I don't think that's a coincidence. I've color coded 7* champs in red, 6* champs in green (ascended champs in a lighter shade) 5* champs in blue, and 4* champs in brown. I'm not sure that helps, but there you go.
These numbers don't fully express the actual difference between rarities and ranks however. When you increase attack by 20% and health by 20%, you don't make the champ 20% stronger. Consider a fight where you are dealing damage and taking damage. You win if you deal enough damage to defeat the defender before you take enough damage to die. There is, in theory, a maximum amount of damage you can deal before you die, if you are constantly losing health. If you increase your attack by 20%, you will deal 20% more damage. But if you increase your health by 20%, you will also deal 20% more damage - because you will live longer and deal more damage before you die. If you increase both, your damage per second goes up and also how many seconds you live to deal damage goes up. The total amount of damage you can deal before you die goes up by a factor of 1.2 x 1.2 =1.44. So in situations where you are challenged and taking damage, increasing damage and health by 20% increases your overall damage dealing ability by almost 50%.
If we scale everyone down to where 5* R1 = 1.0, we can come up with a combined power table that reflects that combined benefit:
And of course:
Now, the order of the champions remains the same, because in effect all we're doing is squaring the numbers. If a < b, a^2 will also be smaller than b^2 (at least here, where power levels start at 1.0 and go up). So the order is the same, but the magnitude of the differences goes up substantially. 7* R2 and 6* R5 ascended look pretty close to 7* R3 in the one dimensional scaling table, but in the combined relative power table 7* R3 is far higher than both. This shows the exponential growth of champion power over time.
The first table does have uses. By focusing on one dimension, we can ask questions like "is a 6* R5 ascended running a 20% champion boost competitive with a 7* R3? The 6* R5 ascended is around 5000 and the 7* R3 is a bit above 6000, so yes, a 6* R5 Ascended champ running a 20% boost is going to be, at least when talking about health and attack, comparable to a 7* R3. Also, if you are in fights where you are pretty sure you aren't going to die, the main advantage of higher rarity is more damage and quicker kills. In that case, more health is not a noteworthy advantage and in those cases the first table better reflects the advantage differences between rarities.
But I think for most players in most reasonably challenging content, it is the second set of data that better quantifies the relative strengths of the different rarities and where ascension places champs, at least before considering the stats ascension does not affect the scaling of, like combat power rate, ability effects, critical rate, etc.
Overall, to me it does look like Ascension roughly does the job it was intended to do. If you're a player that is currently using a mix of 5* and 6* champs, then 5* R5 ascended is at least competitive with a 6* R3, and for such players 6* R4s will likely be still difficult to get. For players using mixes of 6* and 7* champs 6* R5 ascended is very competitive with 7* R2, with 7* R3 champs currently extremely constrained - but those highly expensive and difficult to get rank ups are standing head and shoulders above the rest, as they currently should.
Presumably, almost no one is going to ascend champs that are not either at max rank or one tier below, but I put them all in there for completeness. But I think the best candidates for Ascension are 6* R5, 6* R4, 5* R5, 4* R5, and maybe 6* R3 and 5* R4 (for lower progress players). i would not recommend ascending other ranks.
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That's my pointless story in 1 sentence.
If we consider the difference between 4* champs and a 5* champ at base level is x/y, I assume the difference between 5* champ and 6* champ will be the same x/y right? Then 6* champ and 7* champ will have the same x/y difference ratio is attack and health. So the pattern I mentioned in the above paragraph must stay true right? @DNA3000
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Here's the power scaling for a set of champs. I've scaled all the numbers to be relative to 4* R3 = 1.0 to normalize the scaling values. I specifically tried to pick a wide range of champs across years of release and various prestige and attack emphasis:
Sunspot diverges significantly from the rest. Here it is in graph form:
Everyone pretty much overlaps each other, except Sunspot who diverges significantly from everyone else, especially at the jump from 6* to 7*.
This is what the rarity ranks look like for Sunspot, in descending order, ranked by attack scaling:
It is not a huge difference, about five percentage points of attack or so, but it is there.
The fact that everyone lands almost exactly at 9.0 at 7* R3 suggests to me that at some point someone decided to do something about the irregular scaling, both for big outliers like Sunspot and small deviations in other champs, and tried to make 7* R3 the place where everyone ends at the same starting point (relatively speaking). Ascendancy may have had something to do with that.
I know took him to R3 but still it didn’t seem to bring much change
I’m worried if it’s stats will differ from the one ascended after taking to r3 or any other higher rank
Does ascending at a lower rank differ from ascending at a higher one?